A hybrid vehicle which can distribute power of an internal combustion engine to a first motor generator and a driving wheel by a differential mechanism, such as a planetary gear mechanism, and can output power of a second motor generator to the driving wheel is known. As a control device of such a vehicle, a control device which allows the vehicle to travel in acceleration/coasting travel, in which acceleration travel for driving the driving wheel with power of the internal combustion engine to accelerate the vehicle and coasting travel for stopping the internal combustion engine and allowing the vehicle to coast are repeatedly performed within a predetermined vehicle speed range is known. For example, a control device which, when the thermal efficiency of the internal combustion engine during travel of the vehicle in acceleration/coasting travel is higher than during travel of the vehicle at a constant speed, allows the vehicle in acceleration/coasting travel is known (see PTL 1). In addition, PTL 2 is also the prior art document relating to the invention.